In the ITU Telecommunication Standardization Sector (ITU-T) T.81 and the International Standards Organization (ISO)/International Electrotechnical Commission (IEC) 10918-1 recommended by the ITU-T and the ISO/IEC (hereinafter, “Joint Photographic Experts Group (JPEG)”), a quantization is performed uniformly across an entire frequency domain when performing the quantization (encoding) of transform coefficients on the same quantization scale. In the JPEG, because the human visual feature is relatively insensitive to a high-frequency domain, a coarse quantization is generally performed for a high-frequency component compared with a low-frequency component, by performing a weighting with respect to each frequency domain using a coefficient table called a quantization matrix. The quantization matrix using such human visual feature is designed to minimize an encoding distortion by assuming a distribution of discrete cosine transform (DCT) coefficients as a Laplace distribution.
Even in a conventional video encoding method such as ISO/IEC MPEG-1, 2, 4 and ITU-T H. 261, H. 263, a reduction of a code amount of the transform coefficients is performed by performing the quantization with respect to orthogonal-transformed DCT coefficients. In more recent years, a video encoding method with a greatly improved encoding efficiency has been recommended by the ITU-T and the ISO/IEC as the ITU-T Rec. H. 264 and ISO/IEC 14496-10 (hereinafter, “H. 264”). In the H. 264 high profile, it is configured that a total of eight different quantization matrices can be held with respect to each encoding mode (intra-picture prediction and inter-picture prediction) and each signal (luminance signal and color-difference signal), in association with two types of transform quantization block size (4×4 pixel block and 8×8 pixel block).
Various technologies have been proposed so far to make use of the characteristics of the quantization matrix that the quantization scale can be changed with respect to each frequency position. For instance, a method of designing a quantization matrix taking the visual feature into consideration is proposed in Y. Chen, “Fast Computation of Perceptually Optimal Quantization Matrix for Mpeg-2 Intra Pictures”, ICIP-98, pp. 419-422, October 1998. Furthermore, a method of designing a quantization matrix with a high image dependency to improve the encoding efficiency based on an optimization of an encoding distortion D and a code amount R is proposed in S. W. Wu, “Rate-Constrained Picture-Adaptive Quantization for JPEG Baseline Coders”, ICASP-93, pp. 389-392, April 1993. In addition, a technology for simplifying a design of a quantization matrix by modeling the quantization matrix is proposed in J. Lee, “Rate-Distortion Optimization of Parameterized Quantization Matrix for MPEG-2 Encoding”, ICIP-98, pp. 383-386, October 1998.
However, with the method proposed by Y. Chen, it cannot be said that the quantization matrix is optimally designed from a view point of the encoding efficiency because the actual code amount is not considered in the method, leaving a possibility of performing an inefficient encoding. Furthermore, the method proposed by S. W. Wu is not practically useful because a re-encoding process is required with respect to each frequency position which necessitates a relatively large process cost. In addition, the technology proposed by J. Lee is not practically useful, either, because a massive number of combinations of parameters necessary for the modeling are present which necessitates a relatively large process cost similarly to the method proposed by S. W. Wu.